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Operations research is a vast branch of mathematics which encompasses many diverse areas of minimization and optimization. Thousands of books have been written worldwide on ...

The Zermelo-Fraenkel axioms are the basis for Zermelo-Fraenkel set theory. In the following (Jech 1997, p. 1), exists stands for exists, forall means for all, in stands for ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

A flow defined analogously to the axiom A diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

A transformation which is one-to-one and a surjection (i.e., "onto").

A clear-cut way of describing every object in a class in a one-to-one manner.

If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of ...

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time ...

A multivalued function, also known as a multiple-valued function (Knopp 1996, part 1 p. 103), is a "function" that assumes two or more distinct values in its range for at ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...